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“Our guiding light needs to be our focus on creating a more secure economy for hard-working American families, with smart investments now and for the next generation,” Mr. Benenson said. “Even amid a cascade of news cycles focused on the Affordable Care Act, Syria, the government shutdown and the NSA, voters’ primary focus has never shifted from their economic well-being and financial security.”

He added, “We need to align Democrats with a future-oriented agenda that focuses on the issues that matter to families across the country — strengthening the economy, creating jobs, investing in education, promoting a living wage — and not getting caught up in inside-the-Beltway political dramas that have little bearing on their immediate well-being.”

Although some Republicans say they can make Obamacare the top campaign issue, Mr. Winston has said the party needs to offer an alternative for improving the health care system.

House Republicans have offered several bills designed to make health insurance more affordable, most of them by using the tax code to put more money into pockets with the requirement that it be spent on health care.

A proposal from the conservative Republican Study Committee with 100 co-sponsors, would give a $7,500 deduction to individuals and a $20,000 deduction to families.

A proposal by Rep. Tom Price, Georgia Republican, offers a maximum tax credit of $5,000 for families making up to 200 percent of the federal poverty level, or about $47,000 a year.